1. 8 + (-6) = ?
= ?

3. As you will remember from previous lessons, we can add integers using a number line. Remember if the number is positive we move right and if the number is negative we move left.
For example, in this problem, 4 is negative so we move left 4 and then 6 is positive so we move right 6 and we end up at positive 2.

4. You will remember from previous lessons that absolute value is a number’s distance from zero.
The absolute value of -3 is 3 because -3 is 3 units away from zero. Remember when we are talking about distance, distance is always positive no matter what direction you are moving in. So whenever you take the absolute value of a number, your answer will always be positive.

5. A common mistake that students will make is moving in the wrong direction.
Let’s take -5. The number 5 tells you the distance you will be traveling. You will be traveling 5 units. The positive or negative sign tells you which direction you will be moving. Since 5 is negative, you will be moving left 5.
Just remember, if a number is positive, move to the right and if a number is negative, move to the left.

6. Looking at these two examples: 8 + (-6) and what do you notice about the numbers? One is positive and one is negative.
In this lesson we are going to look at addition problems that have two numbers with different signs.
Let’s first take a look at these problems on a number line. So for the first problem, starting at zero, I need to go right 8 because the 8 is positive. Then I will go left six since the 6 is negative. I end up at +2.
For the second problem, starting at zero, I’m going to go left 10 and right 6. I end up at -4.
What do we notice about the arrows on these number lines? They are going in opposite directions.
Because they are going in opposite directions we are finding the difference between the two numbers. And you remember that to find the difference you subtract. So these addition problems are actually going to turn into subtraction problems.
Another thing we need to remember is that we are working with distance and the number is always positive.
So in the first problem we have a distance of 8 and a distance of 6. (Remember -6 has a distance of 6 in the negative direction but when determining the difference we are not worried about the direction only the distance) So let’s subtract 8 – 6 and get 2.
In the second problem, we have a distance of 10 and a distance of 6. So 10 – 6 is 4.
So we’ve determined the distance, now let’s determine the direction. For the first problem, did we travel farther in the positive direction or negative direction? Well I went 8 units right and only backtracked 6 units left, so we traveled farther in the positive direction. So this means our answer will be positive. So 8 + (-6) = +2
And for the second problem, we traveled father in the negative direction (10 is greater than 6) so when we backtrack 6 we still end up in the negative numbers. So our answer is negative 4.

7. Now to do this without a number line, let’s use the following rule:
If two numbers have different signs, subtract the absolute value of each number and take the sign of the number with the largest absolute value.
We are subtracting the absolute value of each number because the absolute value will give us the distance.
So let’s take the absolute value of 2 and get 2 units. The absolute value of -5 is 5 units. Then subtracting 5 -2 gives us 3 units. So the difference between the distance of 5 and 2 is 3 units.
Now the sign of the answer should be the same as the sign of the farthest distance. Since -5 is 5 units from zero and 2 is only 2 units from zero, -5 has the greatest absolute value or distance. So my answer will be the same sign as -5. So my answer is -3.
So 2 + (-5) = -3

10. in the circles so that each side of the triangle adds up to -5.
Place the integers
in the circles so that each side of the triangle adds up to -5.

11. What integer(s) when added to -7 give a sum greater than 0?
What integer(s) when added to -7 give a sum less than 0?
What integer(s) when added to -7 give a sum of 0?

12. -5 6 4 3 2 5 -3 -6

14. -4 + 3
-3 + 4